A mixed-type finite element approximation for radiation problems using fictitious domain method

H. M. Nasir, T. Kako, D. Koyama

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In the finite element approximation of the exterior Helmholt problem, we propose an approximation method to implement the DtN mapping formulated as a pseudo-differential operator on a computational artificial boundary. The method is then combined with the fictitious domain method. Our method directly gives an approximation matrix for the sesqui-linear form for the DtN mapping. The eigenvalues of the approximation matrix are simplified to a closed form and can be computed efficiently by using a continued fraction formula. Solution outside the computational domain and the far-field solution can also be computed efficiently by expressing them as operations of pseudo-differential operators. An inner artificial DtN boundary condition is also implemented by our method. We prove the convergence of the solution of our method and compare the performance with the standard finite element approximation based on the Fourier series expansion of the DtN operator. The efficiency of our method is demonstrated through numerical examples.

Original languageEnglish
Pages (from-to)377-392
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume152
Issue number1-2
DOIs
Publication statusPublished - Mar 1 2003

Fingerprint

Fictitious Domain Method
Finite Element Approximation
Radiation
Fourier series
Matrix Approximation
Mathematical operators
Pseudodifferential Operators
Boundary conditions
Artificial Boundary Conditions
Artificial Boundary
Exterior Problem
Fourier Expansion
Linear Forms
Continued fraction
Far Field
Series Expansion
Approximation Methods
Closed-form
Eigenvalue
Numerical Examples

Keywords

  • Artificial boundary condition
  • DtN mapping
  • Helmholtz equation
  • Mixed-type method
  • Non-local operator

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A mixed-type finite element approximation for radiation problems using fictitious domain method. / Nasir, H. M.; Kako, T.; Koyama, D.

In: Journal of Computational and Applied Mathematics, Vol. 152, No. 1-2, 01.03.2003, p. 377-392.

Research output: Contribution to journalArticle

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